How can I draw a perpendicular line at the middle of another given line in 3D ?

I have three points on a line (X1,Y1,Z1) , (X2,Y2.Z2) and the middle point (Xm,Ym,Zm), I want to draw a line perpendicular to the given line at the middle point

Answer 1

[Benjamin Thompson]

There is actually a plane that is penpendicular to a line in 3D space. You can follow Gram-Schmidt to identify two perpendicular vectors that define the plane. Any linear combination of those two vectors is a line perpendicular to your line.

https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process#:~:text=In%20mathematics%2C%20particularly%20linear%20algebra,with%20the%20standard%20inner%20product.